Answer to the Problem of the Week
for the week of May 23, 2005
Contributed by Kelly Hill

The Nine Digits Problem

Can you determine the values of A, B, C, D, E, F, G, H, and I,
so that the two addition problems below are correct?

You must use each of the nine digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 exactly once.
The same digits must make both problems correct.

      A     B     C                             A     D     G  
  +     D     E     F                         +     B     E     H  
---------------------                     ---------------------
      G     H     I                             C     F     I  

 

Solution to the Problem:

There are two solutions to the problem:

      1     5     7                             1     4     6  
  +     4     8     2                         +     5     8     3  
---------------------                     ---------------------
      6     3     9                             7     2     9  

and

      7     2     9                             7     1     8  
  +     1     3     5                         +     2     3     6  
---------------------                     ---------------------
      8     6     4                             9     5     4  

Correctly solved by:

1. James Alarie (both solutions) University of Michigan -- Flint,
Flint, Michigan
2. Tristan Collins Winchester, Virginia
3. Charles Washington (both solutions) Winchester, Virginia
4. David & Judy Dixon Bennettsville, South Carolina
5. Jeffrey Gaither Winchester, Virginia